What is the derivative of a(b(x-h)^2+k) ?

The derivative of a(b(x-h)^2+k) is 2ab^2(x-h)

What is the first derivative of a(b(x-h)^2+k) ?

The first derivative of a(b(x-h)^2+k) is 2ab^2(x-h)

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\frac{d}{d x} (a (b (x - h))^{2} + k)

2 a b^{2} (x - h)

Solution steps

\frac{d}{d x} (a (b (x - h))^{2} + k)

Simplify

a (b (x - h))^{2} + k : a b^{2} (x - h)^{2} + k

= \frac{d}{d x} (a b^{2} (x - h)^{2} + k)

Treat

a, k, b, h

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a b^{2} (x - h)^{2}) + \frac{d k}{d x}

\frac{d}{d x} (a b^{2} (x - h)^{2}) = 2 a b^{2} (x - h)

\frac{d k}{d x} = 0

= 2 a b^{2} (x - h) + 0

Simplify

= 2 a b^{2} (x - h)

What is the derivative of a(b(x-h)^2+k) ?
The derivative of a(b(x-h)^2+k) is 2ab^2(x-h)
What is the first derivative of a(b(x-h)^2+k) ?
The first derivative of a(b(x-h)^2+k) is 2ab^2(x-h)